Guaranteed Convergence of a High-Gain Input Observer Robust to Measurement Uncertainty: Application to ECR Estimation*

The work presented here first briefly outlines a previously-developed high-gain input observer, which uses an auxiliary variable for estimating an un-steady input. The primary focus of this paper is on new results, namely on analysis of the aforementioned high-gain observer, including guarantees for: (1) robustness to measurement uncertainty, and (2) an upper bound on the convergence rate of the estimation error. In addition, this effort outlines a method for selecting the observer gain based on measurement uncertainty, acceptable steady-state errors, and desired estimation error convergence rates. Finally, this strategy is demonstrated in practice for estimation of the effective compression ratio (ECR) for IC engines incorporating flexible intake valve closure modulation. Convergence tests were performed at five operating conditions and the estimator is shown to converge well within the guaranteed rate of four engine cycles in the presence of up to 10% measurement uncertainty, with an average steady-state error less than roughly one half of a compression ratio.